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Abstract

The accurate modeling of thermal gradients and distortion generated by directed energy deposition additive manufacturing requires a thorough understanding of the underlying physical processes. One area that has the potential to significantly affect the accuracy of thermomechanical simulations is the complex forced convection created by the inert gas jets that are used to deliver metal powder to the melt pool and to shield the laser optics and the molten material. These jets act on part surfaces with higher temperatures than those in similar processes such as welding and consequently have a greater impact on the prevailing heat transfer mechanisms. A methodology is presented here which uses hot-film sensors and constant voltage anemometry to measure the forced convection generated during additive manufacturing processes. This methodology is then demonstrated by characterizing the convection generated by a Precitec^® YC50 deposition head under conditions commonly encountered in additive manufacturing. Surface roughness, nozzle configuration, and surface orientation are shown to have the greatest impact on the convection measurements, while the impact from the flow rate is negligible.

Keywords

Additive manufacturing finite element analysis convection measurement heat transfer directed energy deposition

Introduction

In additive manufacturing (AM), components are produced in a layer-by-layer manner directly from a digital file. Directed energy deposition (DED) is a major subset of currently available AM processes, in which a high-energy density heat source, such as a laser, electron beam, or arc, is used to create a melt pool into which metal powder or wire is injected. The localized heat input and the heat removed through conduction, convection, and radiation create complex thermal gradients. When combined with the contraction of the melt pool during rapid solidification, plastic deformation and residual stress are induced and negatively affect the finished part, causing it to crack or distort. Finite element analysis (FEA) is often used to simulate the thermal cycles and distortion experienced by discrete components during DED and similar processes. However, useful FEA results can only be achieved when the underlying physical processes are accurately captured.

The high-energy density heat source and the resulting distortion modes in DED are very similar to those found in welding. FEA has been used extensively to simulate welding processes,^1–3 and many aspects of these studies are useful in defining models of the DED process. Unfortunately, the convection models used to simulate shielding gas flows in welding may not be useful. During welding, the rate of convective heat transfer from the weld bead to the environment is low compared to the rate of conductive heat transfer from the bead into the part.⁴ As a result, convective heat loss has been excluded in some models,⁵ while natural convection has been applied to all free surfaces in others.^6–10 However, weld models are not very sensitive to convection because of the comparatively short processing times, low bulk temperatures, and the relatively small amount of filler material addition compared to the size of the existing part.

Even though there are similarities with welding, DED processes have unique characteristics that complicate the convective heat transfer conditions. For example, laser-based processes utilize inert gas jets that are much more concentrated than those used in welding. These jets are used to shield the melt pool, protect the laser optics, and deliver powder to the melt pool. Consequently, localized forced convection is generated on the surfaces of the melt pool and the rapidly solidifying material. In addition, the long processing times and high bulk temperatures prevalent during DED processes allow a great deal of heat to be evacuated through convection.¹¹ Furthermore, the role of forced convection becomes more significant when the large surface area of the deposition and the localization of the convection are considered.

Michaleris⁴ demonstrated that the thermal results of FEA models of DED process are sensitive to surface convection. Despite this sensitivity, convection has been inconsistently applied to FEA models of the process. For example, surface convection has been neglected^12–15 or assumed to be equal to natural convection,^16–18 much like the conditions used in the welding literature. Dai and Shaw¹⁹ use an atypically high value of 60 W/m²/K for natural convection, although the motivation for this choice is unclear. Some of the results from these studies were not validated with experiments, while others were validated with small builds that did not allow sufficient time for the convective heat loss to become significant.

Other researchers have included forced convection models in their simulations of laser-based DED processes. Qi et al.²⁰ considered forced convection when modeling laser cladding; however, the value of the coefficient of convection was not reported. Michaleris⁴ approximated the forced convection as a sphere of higher convection surrounding the melt pool, while free convection was applied on all surfaces outside of this sphere. Ghosh and Choi implemented forced convection from the shielding jet using the empirical equation defined by Gardon and Cobonque^{21, 22} and natural convection on all free surfaces not affected by the gas flow.²³ Zekovic et al.²⁴ included the forced convection on a thin wall and substrate caused by four radially symmetric nozzles blowing an argon gas carrying powder onto the deposition zone. Flow modeling software was used to calculate the velocity contours of the gas around the wall and substrate, and analytical relations were used to calculate local coefficient of convection for the velocity. However, none of these convection models have been validated for the processes being modeled.

Heat transfer resulting from gas jets has been experimentally and numerically studied.^25–34 Many of these works have concluded that the heat transfer is dependent upon the velocity of the jet and its turbulence, which is directly affected by the geometry of the nozzle. Researchers have also investigated how the impingement angle affects the heat transfer on a plate.^25–28 Others have studied the velocity field and heat transfer resulting from two coaxial jets^29–33 and the effect of particles in the flow.³⁴ However, these studies are typically performed using nozzles that are designed to achieve desired flow characteristics, not using nozzles designed for industrial applications. The complexity of the laser deposition process introduces a number of other considerations when attempting to quantify coefficients of convection for improved simulation results. For example, the interaction of the shielding and powder delivery jets, the effect of the metal powder in the jet, and the effect of the deposited surface roughness on the rate of heat transfer have unknown impacts on the predicted convection and the accuracy of these deposition process models.

Measurements of the convection generated during deposition processes are required to produce accurate FEA thermal models.⁴ A technique based on the use of hot-film constant voltage anemometry is developed here to measure the heat transfer from the forced convection produced by laser deposition heads. Calibrations are made to then extract the coefficient of convection from the heat dissipated from the sensor. The forced convection is then characterized at multiple locations around the deposition head to generate a map of the forced convection acting on the surface. This technique is demonstrated by characterizing the forced convection from a Precitec^® YC50 deposition head. An integrated distribution of these measurements is compared to the average convection measured using the lumped capacitance method. Convection resulting from jets impinging onto a flat surface or being bisected by a wall is measured to demonstrate the effect of different surface orientations which are common in AM. In addition, the effects of changes in gas flow rate, nozzle configuration, and surface roughness are investigated to illustrate how convection is affected by changes in common processing parameters.

Methodology

A new method is presented here that utilizes hot-film sensors and constant voltage anemometry to obtain the coefficient of convection from heat transfer measurements at locations on a flat surface relative to the deposition head. Typically, these sensors are used to measure gas velocity based on empirically derived relationships that are dependent upon the gas properties. In the method presented here, the coefficient of convection is extracted from the direct measurement of the heat transfer from the sensor. When a voltage is supplied by a Constant Voltage Anemometer (CVA) to a hot-film sensor, the heat generated through resistive heating is dissipated into the environment through convection and radiation and into the substrate through conduction. Each sensor must be calibrated to determine the conductive heat transfer and the effective area over which the radiation and convection occur. The results allow the coefficient of convection ( $h$ ) to be extracted from the measurements. The distribution of $h$ on a surface resulting from a gas flow is then characterized by taking measurements at incremental locations relative to the deposition head.

Calculating $h$ from hot-film anemometry measurements

Constant voltage anemometry is used to measure the steady-state heat transfer from the element of a hot-film sensor into its surroundings, as shown in Figure 1, and defined by the following energy balance

\int_{V_{e}} Q d V - \int_{A_{e}} q_{conv} d A - \int_{A_{e}} q_{rad} d A - \int_{A_{e}} q_{cond} d A = 0

(1)

where $Q$ is the heat source generated within the element with a volume ( $V_{e}$ ) that is dissipated through convection, conduction, and radiation. The corresponding scalar heat fluxes ( $q_{conv}$ , $q_{rad}$ , and $q_{cond}$ ) are assumed to be uniform over the effective area of the element ( $A_{e}$ ) as derived empirically in section “Effective surface area of the element.” Applying an electric current to the element generates heat within it, as defined by

\int_{V_{e}} Q d V = I^{2} R_{e}

(2)

where the variables $R_{e}$ and $I$ are the resistance of the element and the current flowing through it, respectively. The current is calculated using

I = \frac{V_{c}}{R}

(3)

where $V_{c}$ is the constant voltage applied to the circuit. The total resistance of the circuit ( $R$ ) equals the summation of the resistances of the element ( $R_{e}$ ), the sensor leads ( $R_{l}$ ), and the wires connecting the sensor to the anemometer ( $R_{w}$ )

R = R_{e} + R_{l} + R_{w}

(4)

Figure 1.

Energy balance of the sensor element.

The total convective heat flux ( $q_{conv}$ ) is defined by

\int_{A_{e}} q_{conv} d A = A_{e} q_{conv} = {hA}_{e} (T_{e} - T_{amb})

(5)

The variables $T_{e}$ and $T_{amb}$ are the temperature of the element and the ambient temperature, respectively. The total heat flux through radiation ( $q_{rad}$ ) is

\int_{A_{e}} q_{rad} d A = A_{e} q_{rad} = ε σ A_{e} (T_{e}^{4} - T_{amb}^{4})

(6)

where $σ$ is the Stefan–Boltzmann constant and $ε$ is the surface emissivity of the element. The total amount of heat transferred through conduction ( ${\tilde{q}}_{cond}$ ) is

\int_{A_{e}} q_{cond} d A = {\tilde{q}}_{cond}

(7)

The total conductive heat transfer is derived empirically in section “Conduction into the substrate.” As a result, the total energy balance of the sensor is

I^{2} R_{e} - A_{e} q_{conv} - A_{e} q_{rad} - {\tilde{q}}_{cond} = 0

(8)

The total energy balance is maintained despite changes in the heat transfer acting on the sensor element because its resistance changes in response. For example, an increase in the convection acting on the element decreases its temperature. In turn, both the element resistance and the total resistance of the circuit decrease, causing the current flowing through the element to increase and leading to more resistive heating that balances the increase in convective heat transfer. The following equation relates the temperature and resistance of the element

Δ T = T_{e} - T_{amb} = \frac{\frac{R_{e}}{R_{e_{amb}}} - 1}{α}

(9)

The resistance increases from its initial value ( $R_{e_{amb}}$ ) at ambient temperature to the value during the measurement according to the increase in temperature ( $Δ T$ ) and the temperature coefficient of resistance of the element ( $α$ ). The initial resistance of the element must be determined before the measurement. The total resistance of the circuit during the measurement is calculated from the anemometer output signal.

Based on these measurements, the coefficient of convection can be determined using the following relationship

h = \frac{{(\frac{V_{c}}{R})}^{2} (R - R_{l} - R_{w}) - ε σ ({(T_{amb} + Δ T)}^{4} - T_{amb}^{4}) - {\tilde{q}}_{cond}}{A_{e} Δ T}

(10)

The standard deviation of the coefficient of convection ( $s_{h}$ ) is calculated using the propagation of error formulation³⁵

s_{h} = \sqrt{{(\frac{\partial h}{\partial V_{c}})}^{2} s_{V_{c}}^{2} + {(\frac{\partial h}{\partial R})}^{2} s_{R}^{2} + {(\frac{\partial h}{\partial {\tilde{q}}_{cond}})}^{2} s_{{\tilde{q}}_{cond}}^{2} + {(\frac{\partial h}{\partial A_{e}})}^{2} s_{A_{e}}^{2} + {(\frac{\partial h}{\partial Δ T})}^{2} s_{Δ T}^{2}}

(11)

where $s_{V_{c}}$ and $s_{R}$ are the standard deviations of the applied constant voltage and the calculated circuit resistance during the measurement, respectively. The standard deviation of the element temperature ( $s_{Δ T}$ ) is also derived using the propagation of error formulation

s_{Δ T} = \sqrt{{(\frac{\partial Δ T}{\partial R_{e}})}^{2} s_{R_{e}}^{2}}

(12)

where $s_{R_{e}}$ is the standard deviation of the element resistance during the measurement. The variables $s_{{\tilde{q}}_{cond}}$ and $s_{A_{e}}$ are the standard deviations of the differences between the calibration data and the empirically derived functions for the conduction ( ${\tilde{q}}_{cond}$ ) and the effective area ( $A_{e}$ ).

Sensor calibration

Conduction into the substrate

Conduction from the sensor element into the substrate is complex and cannot be easily calculated. Both the thin film onto which the sensor element is deposited and the adhesive used to mount the sensor to the substrate impact the conduction in unknown ways. Empirically derived functions must, therefore, be developed to take into account the variations within the sensors, adhesives, and substrates.

In order to measure the conduction, the sensor must be insulated from convection and radiation. Insulation is used to eliminate the convective and radiative heat transfer components and allow conduction to be measured using the following relationship

I^{2} R_{e} - {\tilde{q}}_{cond} = 0

(13)

A range of constant voltages are applied to the sensor to heat the element to different temperatures. Measurements of the heat transfer from the element are made at each constant voltage increment once the element temperature has stabilized. It is assumed that the substrate temperature is equal to the ambient temperature ( $T_{amb}$ ) and does not change during the calibration since its thermal mass is orders of magnitude larger than the thermal mass of the element.

The average values of the constant voltage and the output signal during the steady-state measurement at each increment are used to calculate the increase in sensor element temperature ( $Δ T$ ). These values are calculated using the CVA supplied function to calculate the circuit resistance from the output signal and equation (9). Conductive heat transfer is calculated using equation (13). A function is then fit to the data to relate conductive heat transfer to $Δ T$ . The standard deviation of the difference between the data and the fit is used to calculate $s_{{\tilde{q}}_{cond}}$ .

Effective surface area of the element

Resistive heating within the sensor element generates a greater temperature in the element than in the leads. This temperature gradient effectively spreads the heat over a greater area than the nominal area of the element, as demonstrated by O’Donovan et al.³⁶ using a FEA model of a sensor. In the method presented here, the effective surface area is empirically derived (as a function of $Δ T$ ) by performing a series of measurements of the heat transfer at a variety of constant voltages while the substrate is placed in a steady and uniform gas flow, hereafter known as the reference flow. The convection generated by the reference flow is measured using the lumped capacitance method.³⁷ In this method, a thin plate of a known material and geometry is heated to a uniform temperature and then placed in the reference flow. The temperature of the plate is measured as it cools and is used to calculate the average coefficient of convection ( $\bar{h}$ ) acting over the plate. The cooling of the plate with a known volume ( $V$ ), density ( $ρ$ ), and heat capacity ( $c$ ) subjected to convection and radiation is described as

\bar{h} A (T - T_{amb}) + ε σ A (T^{4} - T_{amb}^{4}) = - ρ c V_{\frac{d T}{d t}}

(14)

where $A$ is the exposed surface area of the plate through which convection and radiation occur. Since equation (14) is nonlinear, $\bar{h}$ is calculated using an iterative process to achieve a decay in $T$ that matches the measured temperature decay. Once the average coefficient of convection is found, it can be substituted for $h$ , so that the effective surface area can be calculated.

The lumped capacitance method is valid when the ratio of convection to internal conduction is sufficiently small. This ratio is described by the nondimensional Biot number ( $Bi$ )

Bi = \frac{\bar{h} V}{Ak}

(15)

where $k$ is the thermal conductivity of the plate. The lumped capacitance method is a valid way to measure the average coefficient of convection only when $Bi$ is less than 0.1.³⁷ The Biot number is calculated from all lumped capacitance measurements to prove their validity.

Map the distribution of convection

The distribution of the localized forced convection generated by a deposition head is characterized using measurements made at incremental locations, as shown in Figure 1. When the gas flow is begun, the sensor is allowed to achieve equilibrium, as defined in equation (8). The time required for this to occur is dependent upon the sensor and substrate. Once the output signal from the CVA becomes steady, the constant voltage and the sensor output are recorded and then the mean values and standard deviations of these signals are used to calculate the coefficient of convection ( $h$ ) and the standard deviation of this measurement ( $s_{h}$ ) at this location. The relative position of the deposition head to the sensor is then incrementally changed, and time is allowed for the signals to become steady once again before the signals are recorded, allowing $h$ and $s_{h}$ for the new location to be calculated. This procedure is repeated until the convection distribution acting over the desired surface area is mapped.

Validation of the methodology

Equipment

Demonstration of the convection measurement method is performed using a commercially available Precitec YC50 clad head and nozzles, which are schematically depicted in Figure 2. In this specific design, argon gas flows through the center of the clad head to shield the melt pool and to protect the laser optics positioned upstream from the head. The inner nozzle constricts the flow from a diameter of 42.0 mm at the interface with the head to a diameter of 10.4 mm at the nozzle exit over a length of 60.1 mm, allowing the shield flow to exit the nozzle through an 85-mm² area. Powder and argon gas are delivered to the part through a 2.5-mm-wide circumferential channel in the clad head. The clearance between the outer nozzle and the inner nozzle is 0.7 mm, and the powder delivery flow exits through a 65-mm² area between the inner and outer nozzles. During processing, the bottom of the outer nozzle is positioned at a constant height of 10 mm above the target surface.

Figure 2.

Cross-sectional view of the Precitec^® YC50 head and nozzles.

Senflex^® SF9902 single-element hot-film sensors from Tao of Systems Integration, Inc. are used to measure the convective heat transfer generated by the deposition head. The sensors are chosen because their small element size results in a fine resolution of the measurement distribution. Figure 3 shows a schematic diagram of a characteristic sensor that consists of a nickel element and copper leads. The nickel element, which is nominally 0.20 μm thick, 0.1 mm wide, and 1.4 mm long, has been deposited onto 0.2-mm-thick Upilex^® polyimide film. Copper leads that are nominally 12 μm thick and 0.76 mm wide are also deposited onto the film. Copper wires with diameters of 0.25 mm and lengths between 3.3 and 3.6 m are used to connect the sensors to a four-channel Tao of Systems Integration, Inc. Model 4-600 CVA. The relationship between the output voltage ( $V_{o}$ ) and the total resistance of the circuit ( $R$ ) is given as³⁷

R = \frac{1}{a \frac{V_{o}}{V_{c}} + b}

(16)

where $a$ and $b$ are channel-specific variables that are provided with the CVA.³⁸ The voltage signals from the CVA are acquired using a National Instruments NI 9205 module. Type K thermocouples are used to monitor the ambient temperature of the environment and to measure the temperature of the argon jets at the nozzle outlet. The jet temperature is measured before the convection measurements so that the thermocouple does not affect the flow during those measurements. It is found that the jet temperature is equal to the ambient temperature of the deposition environment. A National Instruments NI 9213 module is used to acquire the thermocouple signals. The acquired thermocouple and voltage signals are recorded in a LabVIEW^® environment at a rate of 20 Hz.

Figure 3.

Senflex^® SF9902 hot-film sensor with dimensions of the nickel element and copper leads: (a) sensor and (b) schematic diagram of sensor with dimensions.

Three sensors are attached to a 222-mm-long, 123-mm-wide, and 3.2-mm-thick plexiglass substrate using MACfilm^® IF-2012 adhesive, as shown in Figure 4. This configuration allows the convection acting on a wall to be measured at different distances from the top edge when the substrate is mounted vertically. A plexiglass substrate was chosen because it has a lower thermal conductivity than the metallic materials typically used in cladding operations. This selection decreases the energy transfer through conduction. A 45° edge is ground into the back edge of the substrate, so that this edge has a minimal impact on the gas flow when the substrate is mounted vertically to bisect the flow. Sensors 1 and 2 are placed 0.8 and 5.4 mm from this edge, respectively. Sensor 3 is mounted near the middle of the substrate, 108.7 mm from the ground edge.

Figure 4.

Schematic diagram of the plexiglass substrate and the three hot-film sensors mounted on it.

Heat loss through conduction

The process described in section “Conduction into the substrate” is used to empirically derive functions that describe the conductive heat loss from each sensor into the plexiglass substrate. Fiberglass insulation, 90 mm thick, is placed on top of the substrate. Measurements are made using constant voltages between 0.3 and 1.0 V, in 0.1-V increments, to heat the nickel elements. At each setting, the energy balance is allowed approximately 30 s to reach equilibrium before $V_{c}$ and $V_{o}$ signals are recorded over a period of approximately 30 s. The mean values of these signals are used to calculate $Δ T$ and ${\tilde{q}}_{cond}$ at each increment. Figure 5 presents the results from these measurements. A second-order polynomial function produced the best fit to the data for each sensor, as shown in the following relationships

{\tilde{q}}_{cond, sensor 1} = - 2.428 e^{- 7} Δ T^{2} + 3.854 e^{- 4} Δ T - 2.876 e^{- 3}

(17)

{\tilde{q}}_{cond, sensor 2} = - 2.174 e^{- 7} Δ T^{2} + 4.072 e^{- 4} Δ T - 3.491 e^{- 3}

(18)

{\tilde{q}}_{cond, sensor 3} = - 4.489 e^{- 7} Δ T^{2} + 5.241 e^{- 4} Δ T - 1.149 e^{- 3}

(19)

Figure 5.

For each sensor, the heat loss through conduction is dependent on the element temperature: (a) sensor 1, (b) sensor 2, and (c) sensor 3.

The quality of these fits is described by the difference between the calculations and measurements at one standard deviation. These values are less than 1% of the rate of conduction into the substrate from each sensor.

Effective surface area

The effective area of each sensor is found using the process described in section “Effective surface area of the element” using aluminum, copper, and steel plates. Different plates are used to demonstrate that this calibration is independent of the chosen plate material. Table 1 presents the properties of these plates. Each plate is heated and then placed on an insulated fixture, to restrict the heat loss to one side of the plate, and cooled in four different airflows. The chosen reference flows have average velocities that are similar to the output from the deposition head. Three of the reference flows, with velocities of 1.3, 1.8, and 2.5 m/s, are parallel to the plate. A fourth reference flow with a velocity of 2.8 m/s is perpendicular to the cooling plate.

Table 1.

Properties of the plates used in the modified lumped capacitance analysis to determine the effective surface area of each sensor element.

	Al 6061-T6	Commercially pure Cu	A36 steel
$ρ$ (kg/m³)	2710	8470	7833
$c_{p}$ (J/kg/K)	896	397	465
$k$ (W/m/K)	167	386	54
$A$ (m²)	$20.5 e^{- 3}$	$19.8 e^{- 3}$	$19.5 e^{- 3}$
$V$ (m³)	$65.2 e^{- 6}$	$62.8 e^{- 6}$	$124 e^{- 6}$
$L_{c}$ (mm)	3.18	3.17	6.36
$ε$	0.09	0.038	0.79

Table 2 presents the results of the modified lumped capacitance measurements. The negligible differences between the measurements made using each plate indicate that the plate material has no impact on the calibration. The mean and standard deviation of the average coefficient of convection is calculated for each airflow. Considering the difference in properties of the three plates, the small standard deviation in each airflow illustrates the consistency of the lumped capacitance method to determine the average convection resulting from each reference flow condition.

Table 2.

Results of the modified lumped capacitance measurements to determine the effective surface area of each sensor element.

	Parallel to a 1.3-m/s airflow			Parallel to a 1.8-m/s airflow			Parallel to a 2.5-m/s airflow			Perpendicular to a 2.8-m/s airflow
Plate	Al	Cu	Steel	Al	Cu	Steel	Al	Cu	Steel	Al	Cu	Steel
$\bar{h}$ (W/m²/K)	27.5	25.4	26.6	32.5	29.4	30.4	39.5	36.8	38.5	25.4	22.5	23.6
$Bi$	5e⁻⁴	2e⁻⁴	4e⁻³	7e⁻⁴	3e⁻⁴	4e⁻³	8e⁻⁴	3e⁻⁴	5e⁻³	7e⁻⁴	3e⁻⁴	4e⁻³
Average $\bar{h}$ (W/m²/K)	$27 \pm 1$			$31 \pm 2$			$38 \pm 1$			$24 \pm 1$

After the average convection resulting from each reference flow is determined, measurements are made using the hot-film sensors with the substrate placed in the insulated fixture. Measurements are made in each airflow using constant voltages ( $V_{c}$ ), ranging from 0.3 to 1.0 V in 0.1-V increments, to heat the element to a range of temperatures. The mean value of each signal and the average coefficient of convection from Table 2 are used to calculate the effective area using equation (5) for each flow condition. Figure 6 presents the resulting data to which second-order exponential equations are fit to the data to develop functions to describe $A_{e}$ for each sensor, as well as the standard deviations of the difference between the data and these functions

A_{e, sensor 1} = 5.66 \overset{- 0.017 Δ T}{\exp} + 4.15 \overset{- 0.003 Δ T}{\exp}

(20)

A_{e, sensor 2} = 22.45 \overset{- 0.065 Δ T}{\exp} + 5.48 \overset{- 0.005 Δ T}{\exp}

(21)

A_{e, sensor 3} = 3.02 \overset{- 0.013 Δ T}{\exp} + 0.56 \overset{- 0.001 Δ T}{\exp}

(22)

Figure 6.

Measurement data and the corresponding second-order exponential fit used to calculate the effective area for each sensor: (a) sensor 1, (b) sensor 2, and (c) sensor 3.

Measurement cases

Table 3 presents the hot-film constant voltage anemometry measurement cases, and Figure 7 illustrates the different measurement setups used to map the convection generated by the deposition head. Powder is not included during these hot-film measurements because its abrasive nature could deteriorate the nickel element, changing its resistance and affecting the calculation of the coefficient of convection according to equation (10).

Table 3.

Cases used to measure the distribution of $h$ resulting from different argon flow conditions.

Case	Jet	Surface	Shielding flow (L/min)	Powder delivery flow (L/min)
1	Impinging	Smooth	9	9
2	Impinging	Smooth	19	19
3	Impinging	Smooth	9	0
4	Impinging	Smooth	19	0
5	Impinging	Rough	9	9
6	Parallel	Smooth	9	9

Figure 7.

Illustrations of the experimental setups: (a) the distribution of $h$ resulting from an impinging argon jet is measured in cases 1 through 5 and (b) the distribution of $h$ on a vertical wall when it bisects the argon jet is measured in case 6.

The hot-film measurement method is used to map the distribution of $h$ resulting from the argon jet impinging onto a surface in cases 1 through 5. The experimental setup is presented in Figure 6. The plexiglass substrate is placed on the horizontal X-Y plane, with the sensor 3 located at the origin of the reference frame. In this orientation, the dimensions of the nickel element limit the nominal spatial resolution to 0.1 mm in the X-axis and 1.45 mm in the Y-axis. The effective surface area of the element makes the actual resolution slightly larger. Both the shielding and powder delivery flows are used in cases 1 and 2, with rates of 9 and 19 L/min, respectively. Cases 3 and 4 are performed to investigate the heat transfer when the head is used for laser processes that do not require powder to be injected into the melt pool, such as wire-based deposition. The rate of the shielding flow in case 3 is 9 L/min and the rate in case 4 is 19 L/min. Measurements are performed along the X- and Y-axes in case 1 to identify any axial asymmetry in the distribution of the convective cooling, and all other case measurements are performed only along the X-axis to simplify the analysis.

In case 5, Shurtape^® anti-skid tread tape is applied to the plexiglass substrate to simulate the rough surface typically produced in a powder-based deposition. Figure 8 shows the similarity of a powder-clad surface¹¹ and the tread tape. The roughness of these two surfaces was measured by Gouge et al.³⁹ using optical profilometry. The roughness average ( $R_{a}$ ) values of the clad and tape are 26.91 and 25.62 μm, respectively. Although these averages are similar, the standard deviation of the tape measurement (11.17 μm) is larger than the measurement of the clad (1.17 μm). Furthermore, the undulations visible in the clad surface generated by successive clad tracks are not represented in the tape. However, for the purpose of this study, the roughness of the tape does not need to be identical to that of a clad surface; it is only used to demonstrate the potential difference between a rough surface, similar to the one produced through powder cladding, and a smooth surface.

Figure 8.

Images of (a) the clad surface produced in Heigel et al.¹¹ using a laser power of 2.5 kW, a travel speed of 10.6 mm/s, a hatch spacing of 2 mm, and a powder flow delivery rate of 19 g/min and (b) the Shurtape^® anti-skid tread tape that is applied to the surface around the sensor to approximate the clad surface.

In case 6, the distribution of $h$ on the face of a vertical wall resulting from a parallel jet is measured using the hot-film method. As shown in Figure 7(b), the shielding and powder delivery jets are emitted by the nozzle while the top edge of the substrate, with the 45° edge, bisects the argon jet. The convection acting at increasing distances from the top edge is measured using the three sensors. In this orientation, the plexiglass substrate is fixed in the vertical X-Z plane. The dimensions of the sensors limit the nominal resolution to 1.45 mm in the X-axis and 0.1 mm in the Z-axis.

Comparison with the lumped capacitance method

Modified lumped capacitance measurements are performed, using copper and aluminum plates, to verify the hot-film measurement method. Both argon flows are used to create an impinging jet to cool the plates, and the rate of each flow is 9 L/min. Each plate is heated to a temperature greater than 100 °C and then placed on an insulated fixture under the deposition head, as shown in Figure 9. Measurements are made with and without the inclusion of powder in the flow to determine its impact on the measurement of the average coefficient of convection.

Figure 9.

Illustration of the modified lumped capacitance method.

Effect of metal powder in the flow

It is necessary to determine the impact of powder on the coefficient of convection because it cannot be used during the hot-film anemometry measurements. Table 4 presents the average coefficient of convection ( $\bar{h}$ ) measured using a modification of the lumped capacitance method, for the coaxial jets impinging upon the surface of each metal plate. The jets are produced by the two argon flows, each with a rate of 9 L/min (case 1). When no powder is included in the argon flow, the measured values of $\bar{h}$ are 65.6 W/m²/K using the aluminum plate and 66.5 W/m²/K using the copper plate. When Inconel^® 625 powder, with a particle size distribution between 44 and 149 μm, is delivered at a rate of 19 g/min, the measured values of $\bar{h}$ are 65.1 and 65.4 W/m²/K. The inclusion of powder changes $\bar{h}$ by only 0.7% and 1.6% for each plate, indicating that the powder has a negligible effect on the average convective heat transfer.

Table 4.

Values of $\bar{h}$ measured using the lumped capacitance method, resulting from an impinging jet created by a 9-L/min shield flow and a 9-L/min powder delivery flow (case 1).

Material	Al 6061-T6		Commercially pure Cu
Dimensions (mm)	49.33 × 46.43 × 3.12		50.01 × 50.08 × 3.18
Powder rate (g/min)	0	19	0	19
$\bar{h}$ (W/m²/K)	65.6	65.1	66.5	65.4
$Bi$	1e⁻³	1e⁻³	5e⁻⁴	5e⁻⁴

Comparison between the methods

The surface convection resulting from an impinging jet is characterized by taking measurements at discrete points on the X- and Y-axes. By compiling these individual measurements, the distribution of the coefficient of convection can be compared to the average coefficient of convection measured using the lumped capacitance method. Figure 10 presents the hot-film measurement results from case 1 in which both the shielding and powder delivery argon jets impinge upon the substrate at a rate of 9 L/min. Figure 9 shows that $h$ decays from a maximum value of $105 \pm 9 {W / m}^{2} / K$ at the impingement point (X = 0 mm) to a value of $32 \pm 3 {W / m}^{2} / K$ at the edges. The decrease in $h$ is more gradual on the negative X-axis than on the positive X-axis. Figure 9 shows that two local maxima of $96 \pm 7$ and $117 \pm 8 {W / m}^{2} / K$ , separated by 12 mm, occur on the Y-axis. A minimum value of $75 \pm 6 {W / m}^{2} / K$ is measured between these two maxima.

Figure 10.

Results from case 1 in which the shielding and powder delivery jet impinge upon the substrate. The rate of each flow is 9 L/min. Measurements are performed in 3-mm increments along (a) the X-axis and (b) the Y-axis.

The hot-film measurement results are compared to those obtained using the lumped capacitance method. To make this comparison, the average coefficient of convection ( $\bar{h}$ ) acting over the area corresponding to the surface of each metal plate is calculated. First, a quadratic polynomial fit is applied to the data, and $\bar{h}$ is calculated as the average of this surface fit. The anemometry measurements produce values that are 3%–5% greater than those measured using the lumped capacitance method. This small difference can be attributed to the nature of the two measurement methods. During the lumped capacitance method, the argon jet impinges upon the metal plate, causing the gas to deflect and flow across its surface. As it flows over the surface, the temperature of the gas increases as it extracts heat from the plate, reducing the rate of heat transfer acting nearer the edges of the plate. In the anemometry measurements, the gas does not extract heat from the plexiglass substrate as it flows toward the heated sensor element at each measurement location.

Measurement results and discussion

The impact of flow rate on convection is investigated by first comparing the two cases along the X-axis with different argon flow rates supplying each jet. Figure 11 compares the results measured in case 1 with those obtained in case 2, in which both the shielding and powder delivery argon jets impinge upon the substrate at a rate of 19 L/min. This flow rate is approximately twice the flow rate used in case 1. The value of $h$ resulting from the 19-L/min flows decays from a value of $107 \pm 8 {W / m}^{2} / K$ to a value of approximately 34 W/m²/K at the outermost measurement locations. The decrease in $h$ is more gradual on the negative axis than the positive axis.

Figure 11.

Comparison of the convection generated by two different flow rates for each argon flow.

Increasing the flow rate supplying each jet has little effect on the convection generated by the deposition head. Figure 11 shows that increasing the rate of each flow from 9 L/min in case 1 to 19 L/min in case 2 increases the maximum measured value of $h$ by only 2 W/m²/K. In addition, the values of $h$ measured at the outermost locations also increase by 1 W/m²/K. These differences are within the uncertainty of the measurements.

Figure 12 presents the results from cases 3 and 4 in which only the shielding jet impinges upon the substrate at a rate of 9 and 19 L/min, respectively. In case 3, two local maxima with values of $39 \pm 4$ and $41 \pm 4 {W / m}^{2} / K$ are separated by 15 mm with a local minimum of $28 \pm 3 {W / m}^{2} / K$ between them. The convection decays from these maxima to approximately 19 W/m²/K at the outermost locations. For case 4, values of $52 \pm 4$ and $53 \pm 5 {W / m}^{2} / K$ are measured at the two local maxima. These maxima are separated by 15 mm, in which a local minimum of $34 \pm 4 {W / m}^{2} / K$ is measured. The convection decays from these peaks to approximately 21 W/m²/K at the outer measurement locations. The local minimum at the impingement point in these cases is likely a result of the boundary between laminar and turbulent flows within the jet, which has been shown in the literature to create maximum values away from the impingement point.⁴⁰

Figure 12.

Comparison of the convection generated only by the shielding jet using different flow rates.

Increasing the rate of the shielding flow from 9 L/min in case 3 to 19 L/min in case 4 increases the values of $h$ measured at the peaks by 12 W/m²/K. This increase exceeds the measurement uncertainty. The minimum value between the peaks increases by 6 W/m²/K. However, there is no difference in the measured values of $h$ at the measurement extremes, indicating that changes in the flow rate have no impact on the convection acting away from the deposition head.

Figure 13 presents a comparison of the heat transfer caused by a single impinging jet compared to two coaxial impinging jets. The combined flow rate of the two jets in case 1 is 18 L/min, and the flow rate of the shielding jet in case 4 is 19 L/min. Despite these similar flow rates, the distribution of $h$ in these two cases is very different. The two coaxial jets in case 1 create an asymmetric distribution of $h$ with a single peak. The single jet in case 4 creates a symmetric distribution with two peaks. The values of $h$ measured at the peaks in case 4, which uses only the shielding flow, are 50% less than the peak when both flows are employed in case 1.

Figure 13.

Convection generated by both the shielding and powder delivery jets compared to the convection generated only by the shielding jet.

Although the flow rates of the shielding and powder delivery jets are the same in case 1, the average velocity of the shielding jet as it exits the inner nozzle is 1.8 m/s, whereas the average velocity of the powder delivery jet as it exits the outer nozzle is 2.3 m/s. This difference in velocity creates a shear between the jets that alters the flow structure, as shown by Hwang et al.³³ In that study, two coaxial jets with different exit velocities created vortices, so that their effect on heat transfer could be investigated. It was shown that the induced vortices could increase the rate of heat transfer on the surface. This effect explains the increased distribution of $h$ when both jets are used in case 1 compared to when only the shielding jet is used in case 4.

The impact of surface roughness on convection is investigated by comparing cases 1–5, as shown in Figure 14. In each case, both argon jets impinge upon the surface at a rate of 9 L/min. In case 5, in which the surface surrounding the sensor is rough, the value of $h$ decays from $88 \pm 7$ to approximately 21 W/m²/K. Compared to the smooth surface in case 1, the rough surface in case 5 decreases the maximum value of $h$ by 19 W/m²/K compared to the maximum value in case 1. In addition, the rough surface causes $h$ to decrease more rapidly from the peak value. Finally, the rough surface decreases the measured values of $h$ at the outer locations by 11 W/m²/K. It should be noted that the rough surface in case 5 is approximated using the tread tape, as discussed in section “Measurement cases,” and consequently, the results may vary for an actual clad surface.

Figure 14.

Effect of surface roughness on convection.

The distribution of convection acting on a vertical wall is found by analyzing the results of case 6. Figure 15 presents the results from case 6 in which both argon jets flow parallel to the substrate at a rate of 9 L/min. The jets flow parallel to the wall surface and are bisected by the top edge of the wall. The coefficient of convection is measured at three locations on the wall. The maximum value of $h$ measured by sensor 1, which is located only 0.8 mm from the top edge of the wall, is $58 \pm 4 {W / m}^{2} / K$ . At sensor 2, which is 5.4 mm below the top edge, the maximum measured value is $40 \pm 6 {W / m}^{2} / K$ . The distribution measured by each of these sensors exhibits a second peak of a significantly lesser value than the maximum. The value of $h$ measured by sensor 1 at the extreme locations is $25 \pm 2 {W / m}^{2} / K$ , and the value measured by sensor 2 is $22 \pm 3 {W / m}^{2} / K$ . The distribution of $h$ measured by sensor 3 exhibits a different trend. A maximum value of $36 \pm 4 {W / m}^{2} / K$ , which decays to values of approximately 21 and 32 W/m²/K, is measured by sensor 3.

Figure 15.

Convection acting on a vertical wall in case 6: (a) sensor 1, 0.8 mm below top edge; (b) sensor 2, 5.4 mm below top edge; and (c) sensor 3, 108.7 mm below top edge.

Figure 16 compares the distribution of $h$ resulting from an impinging jet (case 1) and from a bisected parallel jet (case 6). The flow rate of each jet in both cases is 9 L/min. The comparison is made using sensor 1 in case 6, which is closest to the top edge of the plate. The impinging jet causes a greater rate of heat transfer than the parallel jet, which is evident by the fact that the maximum value of $h$ in case 1 is 81% greater than the maximum value in case 6. The distribution of $h$ is different between these two cases. A double peak is created by the parallel flow in case 6, whereas a single peak is created by the impinging jet in case 1. In the literature, impinging jets which impinge directly onto a surface have been found to induce a greater rate of heat transfer compared to parallel jets or those with a shallower impingement angle.^25–28 The jet in case 1 is deflected by the surface and spreads radially from the impingement point, which results in a higher value of $h$ spreading over a greater area. In contrast, the wall bisects the parallel jet and does not disrupt the flow to the same extent. Although the results in case 6 could vary depending on the different in geometry between the ground edge of the substrate and the top of a deposited wall, the comparison is still noteworthy.

Figure 16.

Comparison of the convection on a horizontal surface compared to the convection near the top edge of a vertical wall.

Conclusion

A method using hot-film constant voltage anemometry to measure the heat transfer from the sensor into the environment is developed to characterize the surface convection contribution from the shielding and powder delivery systems used in laser-based AM processes. Calibrations are performed, so that the coefficient of convection can be extracted from the heat transfer measurement. The distribution of the forced convection is mapped by incrementally taking measurements at different locations relative to the deposition head. By comparing its results to those obtained using a modified lumped capacitance measurement, the method is shown to be valid. The modified lumped capacitance measurement is also used to demonstrate that excluding powder during the hot-film anemometry measurement has little impact on the results.

The method is then demonstrated by characterizing the convection generated by a Precitec YC50 deposition head. It is found for this application that the distribution of convection is affected by a variety of factors:

Increasing the flow rate minimally affects the surface convection.

The surface orientation significantly affects the distribution of convection. The convection generated on a wall is more concentrated and has a lower magnitude than compared to the convection acting on a horizontal surface.

Convection is dependent upon the nozzle configuration. More convection is generated when the powder delivery flow is included in the jet, as would be used during a powder deposition, than when only the shielding jet is used, as would be used during a wire deposition.

A rough surface decreases the convection distribution.

These results are specific for the deposition head used in this study. The hot-film constant voltage anemometry method must be used to measure the convection generated by other deposition heads, since the design of other deposition heads could affect the gas flow and alter the convection distribution.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research and/or authorship of this article: J.C. Heigel is supported by the National Science Foundation under grant no. DGE1255832. This article is based upon work supported by the Office of Naval Research through the Naval Sea Systems Command under contract no. N00024-02-D-6604, delivery order no. 0611. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the Office of Naval Research or the National Science Foundation.

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Measurement of forced surface convection in directed energy deposition additive manufacturing

Abstract

Keywords

Introduction

Methodology

Calculating h from hot-film anemometry measurements

Sensor calibration

Conduction into the substrate

Effective surface area of the element

Map the distribution of convection

Validation of the methodology

Equipment

Heat loss through conduction

Effective surface area

Measurement cases

Comparison with the lumped capacitance method

Effect of metal powder in the flow

Comparison between the methods

Measurement results and discussion

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References

Calculating $h$ from hot-film anemometry measurements